{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f04dd603-a2d1-48ce-8c17-9f1dba8de1ee",
   "metadata": {},
   "source": [
    "Chapter 02\n",
    "\n",
    "# 矩阵转置\n",
    "《线性代数》 | 鸢尾花书：数学不难"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccafb456-2453-4c82-8a65-b1963a370cb2",
   "metadata": {},
   "source": [
    "这段代码的核心是对一个随机整数矩阵 $A$ 进行转置操作，并使用 `seaborn.heatmap` 进行可视化，以直观展示数据的结构及其变化。以下是详细的数学分析：\n",
    "\n",
    "### **1. 矩阵 $A$ 的初始化**\n",
    "代码首先使用 `numpy` 生成一个 $5 \\times 12$ 的随机整数矩阵 $A$，其中元素的取值范围是 $[0,9]$：\n",
    "\\[\n",
    "A = \\begin{bmatrix} \n",
    "a_{11} & a_{12} & \\dots & a_{1,12} \\\\ \n",
    "a_{21} & a_{22} & \\dots & a_{2,12} \\\\ \n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\ \n",
    "a_{51} & a_{52} & \\dots & a_{5,12} \n",
    "\\end{bmatrix}\n",
    "\\]\n",
    "其中 $a_{ij} \\in \\mathbb{Z}, \\quad 0 \\leq a_{ij} \\leq 9$。\n",
    "\n",
    "代码使用 `np.random.seed(88)` 确保每次运行时 $A$ 的内容保持一致。然后利用 `seaborn.heatmap` 进行可视化，`cmap='RdYlBu_r'` 设置了颜色映射，使得数值较小的元素偏蓝色，数值较大的元素偏红色。\n",
    "\n",
    "### **2. 矩阵的转置**\n",
    "矩阵 $A$ 的转置 $A^T$ 是交换行列索引得到的矩阵：\n",
    "\\[\n",
    "A^T = \\begin{bmatrix} \n",
    "a_{11} & a_{21} & \\dots & a_{51} \\\\ \n",
    "a_{12} & a_{22} & \\dots & a_{52} \\\\ \n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\ \n",
    "a_{1,12} & a_{2,12} & \\dots & a_{5,12} \n",
    "\\end{bmatrix}\n",
    "\\]\n",
    "其形状从 $5 \\times 12$ 变为 $12 \\times 5$。代码 `A_T = A.T` 完成这个操作，并再次使用 `seaborn.heatmap` 进行可视化。\n",
    "\n",
    "### **3. 行向量的提取及转置**\n",
    "代码通过 `A[[i],:]` 提取第 $i$ 行（即形状保持为 $1 \\times 12$），然后通过 `.T` 进行转置，得到形状为 $12 \\times 1$ 的列向量：\n",
    "\\[\n",
    "A[i,:] =\n",
    "\\begin{bmatrix} a_{i1} & a_{i2} & \\dots & a_{i,12} \\end{bmatrix}\n",
    "\\]\n",
    "转置后变为：\n",
    "\\[\n",
    "A[i,:]^T =\n",
    "\\begin{bmatrix} a_{i1} \\\\ a_{i2} \\\\ \\vdots \\\\ a_{i,12} \\end{bmatrix}\n",
    "\\]\n",
    "可视化展示了这些行向量的不同表现形式。\n",
    "\n",
    "### **4. 列向量的提取及转置**\n",
    "代码通过 `A[:,[j]]` 提取矩阵的第 $j$ 列，生成形状为 $5 \\times 1$ 的矩阵：\n",
    "\\[\n",
    "A[:, j] =\n",
    "\\begin{bmatrix} a_{1j} \\\\ a_{2j} \\\\ \\vdots \\\\ a_{5j} \\end{bmatrix}\n",
    "\\]\n",
    "转置后得到 $1 \\times 5$ 的行向量：\n",
    "\\[\n",
    "A[:, j]^T =\n",
    "\\begin{bmatrix} a_{1j} & a_{2j} & \\dots & a_{5j} \\end{bmatrix}\n",
    "\\]\n",
    "代码依次对不同的列执行此操作，并使用 `seaborn.heatmap` 进行可视化。\n",
    "\n",
    "### **5. 主要数学性质**\n",
    "1. **转置的性质**\n",
    "   - $(A^T)^T = A$\n",
    "   - $(A + B)^T = A^T + B^T$\n",
    "   - $(AB)^T = B^T A^T$（适用于可乘矩阵）\n",
    "\n",
    "2. **矩阵索引**\n",
    "   - $A[i,:]$ 提取第 $i$ 行，形状保持为 $1 \\times n$。\n",
    "   - $A[:,j]$ 提取第 $j$ 列，形状保持为 $m \\times 1$。\n",
    "   - 转置后行变列，列变行。\n",
    "\n",
    "### **6. 可视化的作用**\n",
    "使用 `seaborn.heatmap` 显示矩阵数据，使数据的模式和结构更加直观，特别是矩阵转置前后的形态变化。由于 `annot=True`，图中的每个单元格都会显示其具体的数值，以便观察不同数值的分布情况。\n",
    "\n",
    "### **总结**\n",
    "这段代码主要演示了：\n",
    "- 生成一个 $5 \\times 12$ 的随机整数矩阵；\n",
    "- 计算其转置，并对比原矩阵和转置矩阵的结构；\n",
    "- 提取不同的行向量和列向量，并研究它们的转置特性；\n",
    "- 通过 `seaborn.heatmap` 进行可视化，增强数据的直观理解。\n",
    "\n",
    "整体上，这是一组用于研究矩阵转置及其可视化方法的代码示例，在数据科学和线性代数学习中非常有价值。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25164ae7-96ac-45ce-9ac5-451ae08bbccb",
   "metadata": {},
   "source": [
    "## 初始化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bb93487f-88f3-4ffd-a2c3-c3419f57f288",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4b9060df-7628-486a-afeb-4a77ae357d58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 0, 1, 4, 5, 1, 0, 5, 0, 2, 1, 4],\n",
       "       [7, 9, 7, 7, 6, 6, 3, 1, 0, 8, 6, 0],\n",
       "       [0, 5, 7, 5, 3, 9, 5, 3, 7, 3, 9, 3],\n",
       "       [8, 5, 0, 6, 4, 0, 2, 2, 5, 9, 2, 5],\n",
       "       [6, 6, 1, 1, 8, 6, 1, 2, 1, 7, 4, 3]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(88)  # 保证每次运行生成相同的随机数\n",
    "A = np.random.randint(0, 10, (5, 12))\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "374c696c-5a83-42b5-b7e3-29244ee6dbb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9456c107-3306-48e2-af90-54e497f8b0cf",
   "metadata": {},
   "source": [
    "## 计算矩阵 A 的转置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d1bcc1c4-4ac1-4c8b-88a6-b6780737a454",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 7, 0, 8, 6],\n",
       "       [0, 9, 5, 5, 6],\n",
       "       [1, 7, 7, 0, 1],\n",
       "       [4, 7, 5, 6, 1],\n",
       "       [5, 6, 3, 4, 8],\n",
       "       [1, 6, 9, 0, 6],\n",
       "       [0, 3, 5, 2, 1],\n",
       "       [5, 1, 3, 2, 2],\n",
       "       [0, 0, 7, 5, 1],\n",
       "       [2, 8, 3, 9, 7],\n",
       "       [1, 6, 9, 2, 4],\n",
       "       [4, 0, 3, 5, 3]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_T = A.T\n",
    "A_T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c3a94695-c6ff-44c0-b66c-b72de917daf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A_T, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "186a8bf5-b412-4469-b1c8-0443241379f7",
   "metadata": {},
   "source": [
    "## 行向量的转置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "916b8524-af91-4c86-afd7-a703127b4eca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 0, 1, 4, 5, 1, 0, 5, 0, 2, 1, 4]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[[0],:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a1715d35-3a92-4ea5-905f-3cc2368ad1bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WLcO0adNEp5k5OTkhPDwcL730EgIDA+Hp6Yn3338f+/fvh7+/v+g8Kz8/xrT2+HP69GkRSYrSpYaNn936LEKSJMU9s1CTuXPn4ujRo4p8NhEQEICSkhLU1tYiJycHMTExKCgoUMzAcfbsWcTHx2PHjh1Wz9CUJCoqyvzvoUOHIjw8HAMGDMC7776LxMREgWU3mUwmhIaGIjU1FQAwbNgwlJWVISMjQ5HDxttvv42oqCh4eXmJTrGyefNmbNiwARs3bkRQUBBKSkqQkJAALy8vxMTEiM4zW79+PWJjY9GnTx9otVoMHz4c06dPx6FDh0SntYmPP63rUsOGh4cHtFqt1asYVVVVVtMm/Trz5s3Dtm3bUFhYiL59+4rOsWJra4s77rgDABAaGoqioiK89tprWLNmjeCyG4qLi1FVVYWQkBDzWktLCwoLC5Geng6j0QitViuwsHWOjo4YOnQoTpw4ITrFzGAwWA2RgYGByMnJEVTUttOnT2Pnzp3YsmWL6JRWLVy4EIsXL8bUqVMB3BgwT58+jbS0NEUNGwMGDEBBQQEaGhpQV1cHg8GAxx57DL6+vqLTrPz87q3KykoYDAbzOh9/buhS92zY2toiJCTEfAf4z/Lz8xERESGoSp0kScLcuXOxZcsWfP7554q8uFsjSRKMRqPoDLOxY8eitLQUJSUl5o/Q0FDMmDEDJSUlihw0AMBoNKK8vNxi0xRt5MiRVm+/Pn78OHx8fAQVtS07Oxu9e/dGdHS06JRWNTY2ols3y+1fq9Uq7q2vP3N0dITBYEBNTQ22b9+ORx55RHSSFV9fX+j1eovHn6amJhQUFPDxB13slQ0ASExMxOOPP47Q0FCEh4cjKysLZ86cwZw5c0SnmV27dg0nT540f15RUYGSkhK4ubnB29tbYNlNcXFx2LhxIz744AM4OTmZXy1ycXGBvb294LoblixZgqioKPTr1w/19fXYtGkTdu3ahU8//VR0mpmTk5PVfS6Ojo5wd3dX1P0vCxYswIQJE+Dt7Y2qqiosXboUdXV1inqWO3/+fERERCA1NRVTpkzBgQMHkJWVhaysLNFpFkwmE7KzsxETE4Pu3ZW5xU6YMAHLli2Dt7c3goKCcPjwYaxcuRKxsbGi0yxs374dkiQhICAAJ0+exMKFCxEQEIBZs2YJ6elo705ISEBqair8/f3h7++P1NRUODg4YPr06YrqrK6uxpkzZ/DDDz8AgHmI1+v18v1+Hdnf7yLAG2+8Ifn4+Ei2trbS8OHDFfd2zS+++EICYPURExMjOs2stT4AUnZ2tug0s9jYWPN57tWrlzR27Fhpx44dorM6pMS3vj722GOSwWCQbGxsJC8vL2nSpElSWVmZ6CwrH374oTRkyBBJp9NJgwYNkrKyskQnWdm+fbsEQDp27JjolDbV1dVJ8fHxkre3t2RnZyf5+flJSUlJktFoFJ1mYfPmzZKfn59ka2sr6fV6KS4uTqqtrRXW09HebTKZpOTkZEmv10s6nU667777pNLSUsV1Zmdnt/r15ORk2Zr4J+aJiIhIVl3qng0iIiJSHg4bREREJCsOG0RERCQrDhtEREQkKw4bREREJCsOG0RERCQrDhtEREQkKw4bREREJCsOG0RERCQrDhtEREQkKw4bREREJCsOG0RERCSr/wFmtCdlqFtYrgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[[0],:], cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "54b03774-612c-40a4-a9a7-a5ad550c3cdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[[0],:].T, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5afc68f2-ad2f-4778-a3de-04a3510241bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7, 9, 7, 7, 6, 6, 3, 1, 0, 8, 6, 0]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[[1],:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "53348e51-b960-4db1-baf8-bc6553f53e92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[[1],:], cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c3d6a511-4ac2-4e9d-97a6-92a395f93441",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 6, 1, 1, 8, 6, 1, 2, 1, 7, 4, 3]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[[-1],:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c38ca005-101c-4ccb-9399-f634b90b47de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[[-1],:].T, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a50977e5-9fcc-431c-8ee2-d02fa698cbdf",
   "metadata": {},
   "source": [
    "## 列向量的转置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "3d6c8cb3-d738-4463-8972-28b63fa34940",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8],\n",
       "       [7],\n",
       "       [0],\n",
       "       [8],\n",
       "       [6]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,[0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d144bd8f-e10a-48a7-9816-390d0cc30194",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[0]], cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c10c29d6-4657-47f7-a8ab-8af4730b832e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[0]].T, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "539f9b2b-dcf7-4c1e-9fdc-709bde9a91dc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [9],\n",
       "       [5],\n",
       "       [5],\n",
       "       [6]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,[1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "9ffb42de-86af-48f1-8f91-313eccd1dbf4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[1]], cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "827a88aa-d11e-46f1-bd28-bf578b1563b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[1]].T, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "736eeb60-9362-4d05-9034-cc49f7d5c47e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5],\n",
       "       [1],\n",
       "       [3],\n",
       "       [2],\n",
       "       [2]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,[7]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "8e7fd565-388b-41a0-ae1a-5fbb902c024b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[7]], cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "9036f104-180d-42fa-8798-b29ebfe02df2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[7]].T, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "70595985-26e7-48c0-aa59-348718f4e32d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4],\n",
       "       [0],\n",
       "       [3],\n",
       "       [5],\n",
       "       [3]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,[-1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "078f2e49-412c-4506-afc8-35eb759f41d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[-1]], cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "1ba3c021-72cf-4594-a4c5-02c8a049e364",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(A[:,[0]].T, cmap = 'RdYlBu_r', square = True, \n",
    "            cbar = False, annot = True, vmin = 0, vmax = 9,\n",
    "            linecolor = 'w', linewidths = 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "954b7525-dcef-47cb-af13-40c741ca3891",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "070c3389-8048-43a3-baa7-6666009bce96",
   "metadata": {},
   "source": [
    "作者\t**生姜DrGinger**  \n",
    "脚本\t**生姜DrGinger**  \n",
    "视频\t**崔崔CuiCui**  \n",
    "开源资源\t[**GitHub**](https://github.com/Visualize-ML)  \n",
    "平台\t[**油管**](https://www.youtube.com/@DrGinger_Jiang)\t\t\n",
    "\t\t[**iris小课堂**](https://space.bilibili.com/3546865719052873)\t\t\n",
    "\t\t[**生姜DrGinger**](https://space.bilibili.com/513194466)  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:base] *",
   "language": "python",
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